Answer:
(x + 12)² + (y + 32)² = 1031
Step-by-step explanation:
137 + 64y = -y² - x² - 24x
Arrange the terms in descending powers of x and y.
x² + 24x + y² + 64y = -137
Complete the squares for x and y
(x² + 24x + 144) + (y² + 64y + 1024) = -137 + 144 + 1024
Write the equation as the squares of binomials of x and y
(x + 12)² + (y + 32)² = 1031
This is the equation of a circle with centre at (-12, -32) and radius r = √1031.
